We are given a set v of n variables {x1, x2, . . , xn} and a set c of m weak and strict inequalities between the variables, i. e., inequalities of the form xi  xj or xi < xj . the set c of inequalities is called consistent 1 over the positive integers z+ = {1,2,} i↵ there is an assignment of positive integer values to the variables that satisfies all the inequalities. for example, the set {x1  x3, x2 < x1} is consistent, whereas {x1  x3, x2 < x1, x3 < x2} is not consistent. (a) give an efficient algorithm to determine whether the set c of inequalities is consistent over the positive integers. state precisely the asymptotic running time of your algorithm in terms of n and т. (b) if the set of inequalities has a solution, then it has a unique minimum solution, i. e., a solution in which every variable has the minimum value among all possible solutions. give an efficient algorithm to compute the minimum solution both parts have o(n+ m) solutions. hint: construct a suitable graph and use appropriate algorithms